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ON A CLASS OF SOBOLEV FUNCTIONS AND ITS APPLICATIONS TO HIGHER-ORDER ELLIPTIC EQUATIONS
Published online by Cambridge University Press: 01 June 2008
Abstract
It is well known that higher-order linear elliptic equations with measurable coefficients and higher-order nonlinear elliptic equations with analytic coefficients can admit unbounded solutions, unlike their second-order counterparts. In this work we introduce the concept of approximate truncates for functions in higher-order Sobolev spaces and prove that if a solution of a higher-order linear elliptic equation has an approximate truncate somewhere then it is bounded there.
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- Copyright © 2008 Australian Mathematical Society